Determining resistivity of a formation adjacent to a borehole having casing using multiple electrodes and with resistances being defined between the electrodes

ABSTRACT

Methods of operation of different types of multiple electrode apparatus vertically disposed in a cased well to measure information related to the resistivity of adjacent geological formations from inside the cased well. The multiple electrode apparatus have a minimum of three spaced apart voltage measurement electrodes that electrically engage the interior of the cased well. Measurement information is obtained related to current which is caused to flow from the cased well into the adjacent geological formation. First compensation information is obtained related to a first casing resistance between a first pair of the spaced apart voltage measurement electrodes. Second compensation information is obtained related to a second casing resistance between a second pair of the spaced apart voltage measurement electrodes. The measurement information, and first and second compensation information are used to determine a magnitude related to the adjacent formation resistivity.

This invention was made with Government support under DOE Grant No.DE-FG06-84ER13294, entitled "Validating the Paramagnetic LoggingEffect", Office of Basic Energy Sciences, of the U.S. Department ofEnergy. The government has certain rights in this invention. The basicconcept for the invention described herein was conceived during thefunding provided by the above grant.

Ongoing research to measure resistivity through casing has been providedon a co-funded basis from: (a) U.S. Department of Energy Grant No.DE-FG19-88BC14243 entitled "Proof of Feasibility of Thru CasingResistivity Technology"; (b) U.S. Department of Energy (DOE) Grant No.DE-FG22-90BC14617 entitled "Proof of Concept of Moving Thru CasingResistivity Apparatus"; (c) U.S. Department of Energy Grant No.DE-FG22-93BC14966 entitled "Fabrication and Downhole Testing of MovingThrough Casing Resistivity Apparatus", and (d) Gas Research Institute(GRI) Contract No. 5088-212-1664 entitled "Proof of Feasibility of theThrough Casing Resistivity Technology". The government and the GRI havecertain rights in this invention. The application herein was filedduring periods of time funded by (b) and (c) above.

This application is a Continuation-in-Part application of an earlier,and still pending, Divisional application that is entitled "Methods ofOperation of Apparatus Measuring Formation Resistivity From Within ACased Well Having One Measurement and Two Compensation Steps"; which isSer. No. 07/754,965; which has a filing date of Sep. 4, 1991; and thatissued on Jun. 29, 1993 as U.S. Pat. No. 5,223,794 {"Vail(794)"}. A copyof Ser. No. 07/754,965 is included herein by reference.

Ser. No. 07/754,965 is a Divisional application of an earlierContinuation-in-Part application that is entitled "ElectronicMeasurement Apparatus Movable In A Cased Borehole and Compensating forCasing Resistance Differences"; which is Ser. No. 07/434,886; which hasa filing date of Nov. 13, 1989; and which issued on Dec. 24, 1991 asU.S. Pat. No. 5,075,626 {"Vail(626)"}. Ser. No. 07/434,886 is includedherein by reference.

Ser. No. 07/434,886 is a Continuation-in-Part application of an earlierContinuation-in-Part application having the title of "Methods andApparatus for Measurement of Electronic Properties of GeologicalFormations Through Borehole Casing"; which is Ser. No. 07/089,697; whichhas the Filing Date of Aug. 26, 1987; and which issued on Nov. 21, 1989as U.S. Pat. No. 4,882,542 {"Vail(542)"}. A copy of Ser. No. 07/089,697is included herein by reference.

Ser. No. 07/089,697 is a Continuation-in-Part application of theoriginal parent application having the title "Methods and Apparatus forMeasurement of the Resistivity of Geological Formations from WithinCased Boreholes"; which is Ser. No. 06/927,115; which has the FilingDate of Nov. 4, 1986; and which issued on Apr. 11, 1989 as U.S. Pat. No.4,820,989 {"Vail(989)"}. A copy of Ser. No. 06/927,115 is includedherein by reference.

This invention provides improved methods and apparatus for measurementof the electronic properties of formations such as the resistivities,polarization phenomena, and dielectric constants of geologicalformations and cement layers adjacent to cased boreholes and formeasuring the skin effect of the casing present. The terms "electronicproperties of formations" and "electrochemical properties of formations"are used interchangeably herein.

The oil industry has long sought to measure resistivity through casing.Such resistivity measurements, and measurements of other electrochemicalphenomena, are useful for at least the following purposes: locatingbypassed oil and gas; reservoir evaluation; monitoring water floods;measuring quantitative saturations; cement evaluation; permeabilitymeasurements; and measurements through a drill string attached to adrilling bit. Therefore, measurements of resistivity and otherelectrochemical phenomena through metallic pipes, and steel pipes inparticular, are an important subject in the oil industry. Many U.S.patents have issued in the pertinent Subclass 368 of Class 324 of theUnited States Patent and Trademark Office which address this subject.The following presents a brief description of the particularly relevantprior art presented in the order of descending relative importance.

U.S. patents which have already issued to the inventor in this field arelisted as follows: U.S. Pat. No. 4,820,989 (Ser. No. 06/927,115); U.S.Pat. No. 4,882,542 (Ser. No. 07/089,697); U.S. Pat. No. 5,043,688 (Ser.No. 07/435,273); U.S. Pat. No. 5,043,669 (Ser. No. 07/438,268); U.S.Pat. No. 5,075,626 (Ser. No. 07/434,886); U.S. Pat. No. 5,187,440 (Ser.No. 07/749,136); and Ser. No. 07/754,965 that issued as U.S. Pat. No.5,223,794 on Jun. 29, 1993. These seven U.S. Patents are collectivelyidentified as "the Vail Patents" herein.

The apparatus and methods of operation herein disclosed are embodimentsof the Through Casing Resistivity Tool™ that is abbreviated TCRT™. TheThrough Casing Resistivity Tool™ and TCRT® are Trademarks ofParaMagnetic Logging, Inc. in the United States Patent and TrademarkOffice. ParaMagnetic Logging, Inc. has its principal place of businesslocated at 18730 - 142nd Avenue N. E., Woodinville, Wash., 98072, USA,having telephone number (206) 481-5474.

An important paper concerning the Through Casing Resistivity Tool waspublished recently. Please refer to the article entitled "FormationResistivity Measurements Through Metal Casing", having authors of W. B.Vail, S. T. Momii of ParaMagnetic Logging, Inc., R. Woodhouse ofPetroleum and Earth Science Consulting, M. Alberty and R. C. A. Peveraroof BP Exploration, and J. D. Klein of Arco Exploration and ProductionTechnology which appeared as Paper "F", Volume I, in the Transactions ofthe SPWLA Thirty-Fourth Annual Logging Symposium, Calgary, Alberta,Canada, Jun. 13-16, 1993, sponsored by The Society of Professional WellLog Analysts, Inc. of Houston, Tex. and the Canadian Well LoggingSociety of Calgary, Alberta, Canada (13 pages of text and 8 additionalfigures). Experimental results are presented therein which confirm thatthe apparatus and methods disclosed in Ser. No. 07/434,886 that is U.S.Pat. No. 5,075,626 actually work in practice to measure the resistivityof geological formations adjacent to cased wells. To the author'sknowledge, the SPWLA paper presents the first accurate measurements ofresistivity obtained from within cased wells using any previousexperimental apparatus.

Other recent articles appearing in various publications concerning theThrough Casing Resistivity Tool and/or the Vail Patents include thefollowing: (A) in an article entitled "Electrical Logging:State-of-the-Art" by Robert Maute of the Mobil Research and DevelopmentCorporation, in The Log Analyst, Vol. 33, No. 3, May-June 1992 page212-213; and (B) in an article entitled "Through Casing Resistivity ToolSet for Permian Use" in Improved Recovery Week, Volume 1, No. 32, Sep.28, 1992.

The Vail Patents describe the various embodiments of the Through CasingResistivity Tool (TCRT). Many of these Vail Patents describe embodimentsof apparatus having three or more spaced apart voltage measurementelectrodes which engage the interior of the casing, and which also havecalibration means to calibrate for thickness variations of the casingand for errors in the placements of the voltage measurement electrodes.

U.S. Pat. No. 4,796,186 which issued on Jan. 3, 1989 to Alexander A.Kaufman entitled "Conductivity Determination in a Formation Having aCased Well" also describes apparatus having three or more spaced apartvoltage measurement electrodes which engage the interior of the casingand which also have calibration means to calibrate for thicknessvariations in the casing and for errors in the placements of theelectrodes. This patent has been assigned to ParaMagnetic Logging, Inc.of Woodinville, Wash. In general, different methods of operation andanalysis are described in the Kaufman Patent compared to the VailPatents cited above.

U.S. Pat. No. 4,837,518 which issued on Jun. 6, 1989 to Michael F. Gard,John E. E. Kingman, and James D. Klein, assigned to the AtlanticRichfield Company, entitled "Method and Apparatus for Measuring theElectrical Resistivity of Geologic Formations Through Metal Drill Pipeor Casing", predominantly describes two voltage measurement electrodesand several other current introducing electrodes disposed verticallywithin a cased well which electrically engage the wall of the casing,henceforth referenced as "the Arco Patent". However, the Arco Patentdoes not describe an apparatus having three spaced apart voltagemeasurement electrodes and associated electronics which takes thevoltage differential between two pairs of the three spaced apart voltagemeasurement electrodes to directly measure electronic propertiesadjacent to formations. Nor does the Arco Patent describe an apparatushaving at least three spaced apart voltage measurement electrodeswherein the voltage drops across adjacent pairs of the spaced apartvoltage measurement electrodes are simultaneously measured to directlymeasure electronic properties adjacent to formations. Therefore, theArco Patent does not describe the methods and apparatus disclosedherein.

USSR Patent No. 56,026, which issued on Nov. 30, 1939 to L. M. Alpin,henceforth called the "Alpin Patent", which is entitled "Process of theElectrical Measurement of Well Casings", describes an apparatus whichhas three spaced apart voltage measurement electrodes which positivelyengage the interior of the casing. However, the Alpin Patent does nothave any suitable calibration means to calibrate for thicknessvariations of the casing nor for errors related to the placements of thevoltage measurement electrodes. Therefore, the Alpin Patent does notdescribe the methods and apparatus disclosed herein.

French Patent No. 2,207,278 having a "Date of Deposit" of Nov. 20, 1972(hereinafter "the French Patent") describes apparatus having four spacedapart voltage measurement electrodes which engage the interior ofborehole casing respectively defined as electrodes M, N, K, and L.Various uphole and downhole current introducing electrodes aredescribed. Apparatus and methods of operation are provided thatdetermines the average resistance between electrodes M and L. ThisFrench Patent further explicitly assumes an exponential current flowalong the casing. Voltage measurements across pair MN and KL are thenused to infer certain geological parameters from the assumed exponentialcurrent flow along the casing. However, the French Patent does not teachmeasuring a first casing resistance between electrodes MN, does notteach measuring a second casing resistance between electrodes NK, anddoes not teach measuring a third casing resistance between electrodesKL. The invention herein and other preferred embodiments described inthe Vail Patents teach that it is of importance to measure said first,second, and third resistances to compensate current leakage measurementsfor casing thickness variations and for errors in placements of thevoltage measurement electrodes along the casing to provide accuratemeasurements of current leakage into formation. Further, manyembodiments of the Vail Patents do not require any assumption of theform of current flow along the casing to measure current leakage intoformation. Therefore, for these reasons alone, the French Patent doesnot describe the methods and apparatus disclosed herein. There are manyother differences between various embodiments of the Vail Patents andthe French Patent which are described in great detail in the Statementof Prior Art for Ser. No. 07/754,965 dated Dec. 2, 1991 that is to issueas U.S. Pat. No. 5,223,794 on Jun. 29, 1993.

An abstract of an article entitled "Effectiveness of Resistivity Loggingof Cased Wells by A Six-Electrode Tool" by N. V. Mamedov was referencedin TULSA ABSTRACTS as follows: "IZV.VYSSH.UCHEB, ZAVEDENII, NEFT GAZno.7, pp. 11-15, July 1987. (ISSN 0445-0108; 5 refs; in Russian)",hereinafter the "Russian Article". It is the applicant's understandingfrom an English translation of that Russian Article that the articleitself mathematically predicts the sensitivity of the type tooldescribed in the above defined French Patent. The Russian Article statesthat the tool described in the French Patent will only be show a "weakdependence" on the resistivity of rock adjacent to the cased well. Bycontrast, many embodiments of the Vail Patents, and the inventionherein, provide measurements of leakage current and other parameterswhich are strongly dependent upon the resistivity of the rock adjacentto the cased well. Therefore, this Russian Article does not describe themethods and apparatus disclosed herein.

U.S. Pat. No. 2,729,784, issued on Jan. 3, 1956 having the title of"Method and Apparatus for Electric Well Logging", and U.S. Pat. No.2,891,215 issued on Jun. 16, 1959 having the title of "Method andApparatus for Electric Well Logging", both of which issued in the nameof Robert E. Fearon, henceforth called the "Fearon Patents", describeapparatus also having two pairs of voltage measurement electrodes whichengage the interior of the casing. However, an attempt is made in theFearon Patents to produce a "virtual electrode" on the casing in anattempt to measure leakage current into formation which provides formethods and apparatus which are unrelated to the Kaufman and VailPatents cited above. The Fearon Patents neither provide calibrationmeans, nor do they provide methods similar to those described in eitherthe Kaufman Patent or the Vail Patents, to calibrate for thicknessvariations and errors in the placements of the electrodes. Therefore,the Fearon Patents do not describe the methods and apparatus disclosedherein.

Accordingly, an object of the invention is to provide new and practicalapparatus having three or more spaced apart voltage measurementelectrodes to measure formation resistivity from within cased wells.

It is yet another object of the invention is to provide new methods ofoperation of the multi-electrode apparatus to measure formation fromwithin cased wells which compensates for casing resistance differencesand which compensates for errors in placements of the voltagemeasurement electrodes.

FIG. 1 is a sectional view of one preferred embodiment of the inventionof the Through Casing Resistivity Tool (TCRT) which is marked with thelegend "Prior Art".

FIG. 2 shows ΔI vs. Z which diagrammatically depicts the response of thetool to different formations which is marked with the legend "PriorArt".

FIG. 3 is a sectional view of a preferred embodiment of the inventionwhich shows how V_(o) is to be measured that is marked with the legend"Prior Art".

FIG. 4 is a sectional view of an embodiment of the invention which hasvoltage measurement electrodes which are separated by differentdistances that is marked with the legend "Prior Art".

FIG. 5 is a sectional view of an embodiment of the invention which haselectrodes which are separated by different distances and which showsexplicitly how to measure V_(o) that is marked with the legend "PriorArt".

FIG. 6 is a sectional view of an embodiment of the invention whichprovides multi-frequency operation to compensate for errors ofmeasurement marked with the legend "Prior Art".

FIG. 7 is a sectional view of an embodiment of the invention thateliminates the use of a certain differential amplifier.

FIG. 8 is a sectional view of an embodiment of the invention thatpossesses four spaced apart voltage measurement electrodes.

FIG. 9 is a sectional view of an embodiment of the invention thatpossesses four spaced apart voltage measurement electrodes and extracurrent introducing electrodes.

FIG. 10 is a multi-electrode apparatus designed to keep certain currentsflowing along the casing constant in amplitude in the vicinity of fourspaced apart voltage measurement electrodes used to measure resistivity.

FIG. 11 is a multi-electrode apparatus designed to keep certain currentsflowing along the casing in constant in amplitude in the vicinity ofthree spaced apart voltage measurement electrodes used to measureresistivity.

FIG. 12 is an apparatus having three spaced apart voltage measurementelectrodes and extra current introducing electrodes.

FIG. 13 is functionally identical to FIG. 26 from Ser. No. 07/089,697that is U.S. Pat. No. 4,882,542, showing an apparatus having multiplevoltage measurement electrodes engaging the interior of the casing thatis marked with the legend "Prior Art".

The invention is described in three major different portions of thespecification. In the first major portion of the specification, relevantparts of the text in Ser. No. 07/089,697 now U.S. Pat. No. 4,882,542,{Vail(542)} are repeated herein which describe apparatus defined inFIGS. 1, 3, 4, and 5. The second major portion of the specificationquotes relevant parts of Ser. No. 07/434,886 {Vail(626)} that describethe apparatus defined in FIG. 6. The third major portion of thespecification herein is concerned with providing multi-electrodeapparatus and methods of operation of the multi-electrode apparatus tomeasure formation resistivity from within cased wells that compensatesfor casing resistance differences and for errors in placements of thevarious voltage measurement electrodes. The definitions provided inFIGS. 1 through 6 are used to conveniently define many of the symbolsappearing in FIGS. 7 through 12.

From a technical drafting point of view, FIGS. 1, 2, 3, 4, and 5 in Ser.No. 07/089,697 {Vail(542)}, now U.S. Pat. No. 4,882,542, and in thosecontained in this application are nearly identical. However, the newdrawings have been re-done using computer graphics and the A-4International Size. The following excerpt is taken word-for-word fromSer. No. 07/089,697:

"FIG. 1 shows a typical cased borehole found in an oil field. Theborehole 2 is surrounded with borehole casing 4 which in turn is held inplace by cement 6 in the rock formation 8. An oil bearing strata 10exists adjacent to the cased borehole. The borehole casing may or maynot extend electrically to the surface of the earth 12. A voltage signalgenerator 14 (SG) provides an A.C. voltage via cable 16 to poweramplifier 18 (PA). The signal generator represents a generic voltagesource which includes relatively simple devices such as an oscillator torelatively complex electronics such as an arbitrary waveform generator.The power amplifier 18 is used to conduct A.C. current down insulatedelectrical wire 20 to electrode A which is in electrical contact withthe casing. The current can return to the power amplifier through cable22 using two different paths. If switch SW1 is connected to electrode Bwhich is electrically grounded to the surface of the earth, then currentis conducted primarily from the power amplifier through cable 20 toelectrode A and then through the casing and cement layer andsubsequently through the rock formation back to electrode B andultimately through cable 22 back to the power amplifier. In this case,most of the current is passed through the earth. Alternatively, if SW1is connected to insulated cable 24 which in turn is connected toelectrode F, which is in electrical contact with the casing, thencurrent is passed primarily from electrode A to electrode F along thecasing for a subsequent return to the power amplifier through cable 22.In this case, little current passes through the earth.

Electrodes C, D, and E are in electrical contact with the interior ofcasing. In general, the current flowing along the casing varies withposition. For example, current I_(C) is flowing downward along thecasing at electrode C, current I_(D) is flowing downward at electrode D,and current I_(E) is flowing downward at electrode E. In general,therefore, there is a voltage drop V1 between electrodes C and D whichis amplified differentially with amplifier 26. And the voltagedifference between electrodes D and E, V2, is also amplified withamplifier 28. With switches SW2 and SW3 in their closed position asshown, the outputs of amplifiers 26 and 28 respectively aredifferentially subtracted with amplifier 30. The voltage from amplifier30 is sent to the surface via cable 32 to a phase sensitive detector 34.The phase sensitive detector obtains its reference signal from thesignal generator via cable 36. In addition, digital gain controller 38(GC) digitally controls the gain of amplifier 28 using cable 40 to sendcommands downhole. The gain controller 38 also has the capability toswitch the input leads to amplifier 28 on command, thereby effectivelyreversing the output polarity of the signal emerging from amplifier 28for certain types of measurements.

The total current conducted to electrode A is measured by element 42. Inthe preferred embodiment shown in FIG. 1, the A.C. current used is asymmetric sine wave and therefore in the preferred embodiment, I is the0-peak value of the A.C. current conducted to electrode A. (The 0-peakvalue of a sine wave is 1/2 the peak-to-peak value of the sine wave.)

In general, with SW1 connected to electrode B, current is conductedthrough formation. For example, current ΔI is conducted into formationalong the length 2 L between electrodes C and E. However, if SW1 isconnected to cable 24 and subsequently to electrode F, then no currentis conducted through formation to electrode B. In this case, I_(C)=I_(D) =I_(E) since essentially little current ΔI is conducted intoformation.

It should be noted that if SW1 is connected to electrode B then thecurrent will tend to flow through the formation and not along theborehole casing. Calculations show that for 7 inch O.D. casing with a1/2 inch wall thickness that if the formation resistivity is 1 ohm-meterand the formation is uniform, then approximately half of the currentwill have flowed off the casing and into the formation along a length of320 meters of the casing. For a uniform formation with a resistivity of10 ohm-meters, this length is 1040 meters instead." These lengths arerespectively called "Characteristic Lengths" appropriate for the averageresistivity of the formation and the type of casing used. ACharacteristic Length is related to the specific length of casingnecessary for conducting on approximately one-half the initial currentinto a particular geological formation as described below.

One embodiment of the invention described in Ser. No. 07/089,697{Vail(542)}, now U.S. Pat. No. 4,882,542, provides a preferred method ofoperation for the above apparatus as follows: "The first step inmeasuring the resistivity of the formation is to "balance" the tool. SW1is switched to connect to cable 24 and subsequently to electrode F. ThenA.C. current is passed from electrode A to electrode F thru the boreholecasing. Even though little current is conducted into formation, thevoltages V1 and V2 are in general different because of thicknessvariations of the casing, inaccurate placements of the electrodes, andnumerous other factors. However, the gain of amplifier 28 is adjustedusing the gain controller so that the differential voltage V3 is nulledto zero. (Amplifier 28 may also have phase balancing electronics ifnecessary to achieve null at any given frequency of operation.)Therefore, if the electrodes are subsequently left in the same placeafter balancing for null, spurious effects such as thickness variationsin the casing do not affect the subsequent measurements.

With SW1 then connected to electrode B, the signal generator drives thepower amplifier which conducts current to electrode A which is inelectrical contact with the interior of the borehole casing. A.C.currents from 1 amp o-peak to 30 amps o-peak at a frequency of typically1 Hz are introduced on the casing here. The low frequency operation islimited by electrochemical effects such as polarization phenomena andthe invention can probably be operated down to 0.1 Hz and theresistivity still properly measured. The high frequency operation islimited by skin depth effects of the casing, and an upper frequencylimit of the invention is probably 20 Hz for resistivity measurements.Current is subsequently conducted along the casing, both up and down thecasing from electrode A, and some current passes through the brinesaturated cement surrounding the casing and ultimately through thevarious resistive zones surrounding the casing. The current is thensubsequently returned to the earth's surface through electrode B."

Quoting further from Ser. No. 07/089,697 {Vail(542)}, now U.S. Pat. No.4,882,542: "FIG. 2 shows the differential current conducted intoformation ΔI for different vertical positions z within a steel casedborehole. Z is defined as the position of electrode D in FIG. 1. Itshould be noted that with a voltage applied to electrode A and with SW1connected to electrode B that this situation consequently results in aradially symmetric electric field being applied to the formation whichis approximately perpendicular to the casing. The electrical fieldproduces outward flowing currents such as ΔI in FIG. 1 which areinversely proportional to the resistivity of the formation. Therefore,one may expect discontinuous changes in the current ΔI at the interfacebetween various resistive zones particularly at oil/water and oil/gasboundaries. For example, curve (a) in FIG. 2 shows the results from auniform formation with resistivity ρ₁. Curve (b) shows departures fromcurve (a) when a formation of resistivity ρ₂ and thickness T₂ isintersected where ρ₂ is less than ρ₁. And curve (c) shows the oppositesituation where a formation is intersected with resistivity ρ₃ which isgreater than ρ₁ which has a thickness of T₃. It is obvious that underthese circumstances, ΔI₃ is less than ΔI₁, which is less than ΔI₂.

FIG. 3 shows a detailed method to measure the parameter Vo. ElectrodesA, B, C, D, E, and F have been defined in FIG. 1. All of the numberedelements 2 through 40 have already been defined in FIG. 1. In FIG. 3,the thickness of the casing is τ₁, the thickness of the cement is τ₂,and d is the diameter of the casing. Switches SW1, SW2, and SW3 havealso been defined in FIG. 1. In addition, electrode G is introduced inFIG. 3 which is the voltage measuring reference electrode which is inelectrical contact with the surface of the earth. This electrode is usedas a reference electrode and conducts little current to avoidmeasurement errors associated with current flow.

In addition, SW4 is introduced in FIG. 3 which allows the connection ofcable 24 to one of the three positions: to an open circuit; to electrodeG; or to the top of the borehole casing. And in addition in FIG. 3,switches SW5, SW6, and SW7 have been added which can be operated in thepositions shown. (The apparatus in FIG. 3 can be operated in anidentical manner as that shown in FIG. 1 provided that switches SW2,SW5, SW6, and SW7 are switched into the opposite states as shown in FIG.3 and provided that SW4 is placed in the open circuit position.)

With switches SW2, SW5, SW6, and SW7 operated as shown in FIG. 3, thenthe quantity Vo may be measured. For a given current I conducted toelectrode A, then the casing at that point is elevated in potential withrespect to the zero potential at a hypothetical point which is an"infinite" distance from the casing. Over the interval of the casingbetween electrodes C, D, and E in FIG. 3, there exists an averagepotential over that interval with respect to an infinitely distantreference point. However, the potential measured between only electrodeE and electrode G approximates Vo provided the separation of electrodesA, C, D, and E are less than some critical distance such as 10 metersand provided that electrode G is at a distance exceeding anothercritical distance from the casing such as 10 meters from the boreholecasing. The output of amplifier 28 is determined by the voltagedifference between electrode E and the other input to the amplifierwhich is provided by cable 24. With SW1 connected to electrode B, andSW4 connected to electrode G, cable 24 is essentially at the samepotential as electrode G and Vo is measured appropriately with the phasesensitive detector 34. In many cases, SW4 may instead be connected tothe top of the casing which will work provided electrode A is beyond acritical depth . . . ".

Quoting further from Ser. No. 07/089,697 {Vail(542)}, now U.S. Pat. No.4,882,542: "For the purposes of precise written descriptions of theinvention, electrode A is the upper current conducting electrode whichis in electrical contact with the interior of the borehole casing;electrode B is the current conducting electrode which is in electricalcontact with the surface of the earth; electrodes C, D, and E arevoltage measuring electrodes which are in electrical contact with theinterior of the borehole casing; electrode F is the lower currentconducting electrode which is in electrical contact with the interior ofthe borehole casing; and electrode G is the voltage measuring referenceelectrode which is in electrical contact with the surface of the earth.

Furthermore, V_(o) is called the local casing potential. An example ofan electronics difference means is the combination of amplifiers 26, 28,and 30. The differential current conducted into the formation to bemeasured is ΔI." The differential voltage is that voltage in FIG. 1which is the output of amplifier 30 with SW1 connected to electrode Band with all the other switches in the positions shown.

Further quoting from Ser. No. 07/089,697 {Vail(542)}, now U.S. Pat. No.4,882,542: "FIG. 4 is nearly identical to FIG. 1 except the electrodes Cand D are separated by length L₁, electrodes D and E are separated byL₂, electrodes A and C are separated by L₃ and electrodes E and F areseparated by the distance L₄. In addition, r₁ is the radial distance ofseparation of electrode B from the casing. And Z is the depth from thesurface of the earth to electrode D. FIG. 5 is nearly identical to FIG.3 except here too the distances L₁, L₂, L₃, L₄, r₁, and Z are explicitlyshown. In addition, r₂ is also defined which is the radial distance fromthe casing to electrode G. As will be shown explicitly in lateranalysis, the invention will work well if L₁ and L₂ are not equal. Andfor many types of measurements, the distances L₃ and L₄ are not veryimportant provided that they are not much larger in magnitude than L₁and L₂."

FIG. 6 was first described in Ser. No. 07/434,886 {Vail(626)} whichstates: "For the purpose of logical introduction, the elements in FIG. 6are first briefly compared to those in FIGS. 1-5. Elements No. 2, 4, 6,8, and 10 have already been defined. Electrodes A, B, C, D, E, F, G andthe distances L₁, L₂, L₃, and L₄ have already been described. Thequantities δi₁ and δi₂ have already been defined in the above text.Amplifiers labeled with legends A1, A2, and A3 are analogousrespectively to amplifiers 26, 28, and 30 defined in FIGS. 1, 3, 4, and5. In addition, the apparatus in FIG. 6 provides for the following:

(a) two signal generators labeled with legends "SG 1 at Freq F(1)" and"SG 2 at Freq F(2)";

(b) two power amplifiers labeled with legends "PA 1" and "PA 2";

(c) a total of 5 phase sensitive detectors defined as "PSD 1", "PSD 2","PSD 3", "PSD 4", and "PSD 5", which respectively have inputs formeasurement labeled as "SIG", which have inputs for reference signalslabeled as "REF", which have outputs defined by lines having arrowspointing away from the respective units, and which are capable ofrejecting all signal voltages at frequencies which are not equal to thatprovided by the respective reference signals;

(d) an "Error Difference Amp" so labeled with this legend in FIG. 6;

(e) an instrument which controls gain with voltage, typically called a"voltage controlled gain", which is labeled with legend "VCG";

(f) an additional current conducting electrode labeled with legend "H"(which is a distance L₅ --not shown--above electrode A);

(g) an additional voltage measuring electrode labeled with legend J(which is a distance L₆ --not shown--below electrode F);

(h) current measurement devices, or meters, labeled with legends "I1"and "I2";

(i) and differential voltage amplifier labeled with legend "A4" in FIG.6."

Ser. No. 07/434,886 {Vail(626)}, now U.S. Pat. No. 5,075,626, furtherdescribes various cables labeled with legends respectively 44, 46, 48,50, 52, 54, 56, 58, 60, 62, and 64 whose functions are evident from FIG.6.

Ser. No. 07/434,886 {Vail)626)}, now U.S. Pat. No. 5,075,626, furtherstates: "The outputs of PSD 1, 2, 3, and 4 are recorded on a digitalrecording system 70 labeled with legend "DIG REC SYS". The respectiveoutputs of the phase sensitive detectors are connected to the respectiveinputs of the digital recording system in FIG. 6 according to thelegends labeled with numbers 72, 74, 76, 78, and 80. One such connectionis expressly shown in the case of element no. 72."

Ser. No. 07/434,886 {Vail(626)}, now U.S. Pat. No. 5,075,626, teaches ingreat detail that it is necessary to accurately measure directly, orindirectly, the resistance between electrodes C-D (herein defined as"R1") and the resistance between electrodes D-E (herein defined as "R2")in FIGS. 1, 3, 4, 5 and 6 to precisely measure current leakage intoformation and formation resistivity from within the cased well. Pleaserefer to Equations 1-33 in Ser. No. 07/434,886 {Vail(626)}, now U.S.Pat. No. 5,075,626, for a thorough explanation of this fact. The parentapplication, Ser. No. 06/927,115 {Vail(989)}, now U.S. Pat. No.4,820,989, and the following Continuation-in-Part application Ser. No.07/089,697 {Vail(542)}, now U.S. Pat. No. 4,882,542, taught thatmeasurement of the resistance of the casing between voltage measurementelectrodes that engage the interior of the casing are very important tomeasure formation resistivity from within the casing.

Using various different experimental techniques that result in currentflow along the casing between current conducting electrodes A and F inFIGS. 1, 3, 4, 5, and 6 result in obtaining first compensationinformation related to a first casing resistance defined between voltagemeasurement electrodes C and D. Similarly, using various differentexperimental techniques that result in current flow along the casingbetween current conducting electrodes A and F in FIGS. 1, 3, 4, 5, and 6result in obtaining second compensation information related to a secondcasing resistance between voltage measurement electrodes D and E. FIGS.1, 3, 4, 5, and 6 all provide additional means to cause current to flowinto formation, and the measurements performed while current is flowinginto the formation is called the measurement information related tocurrent flow into formation. Such measurement information is used todetermine a magnitude relating to formation resistivity. FIGS. 7-12 inthe remaining application also provide various means to providemeasurement information, and respectively first and second compensationinformation, along with additional information in several cases.

FIG. 7 is closely related to FIG. 6. However, in FIG. 7, amplifier A3that is shown in FIG. 6, which can be either downhole, or uphole, hasbeen removed. Further, the Error Difference Amp, cable 60, and the VCGhave also been removed. In FIG. 7, the output of amplifier A1 atfrequency F(1) is measured by PSD 4 and the output of amplifier A1 atfrequency F(2) is measured by PSD 2--as was the case in FIG. 6. However,in FIG. 7, the output of amplifier A2 at F(1) is measured by PSD 1 andthe output of amplifier A2 at F(2) is measured by PSD 3. In FIG. 7,current at the frequency of F(1) is conducted into formation resultingin measurement information being obtained from PSD 1 and PSD 4. Currentat the frequency of F(2) is caused to flow along the casing betweenelectrodes H and F to provide compensation for casing thicknessvariations and to provide compensation for errors in the placement ofthe voltage measurement electrodes. First compensation informationrelated to the casing resistance between electrodes C and D is obtainedfrom PSD 2. Second compensation information related to the casingresistance between electrodes D and E is obtained from PSD 3. Analogousalgebra exists for the operation of the apparatus in FIG. 7 to Equations1-33 in Ser. No. 07/434,886, now U.S. Pat. No. 5,075,626, {Vail(626)}that provides compensation for casing resistance differences and forerrors of placements of the three spaced apart voltage measurementelectrodes C, D, and E.

FIG. 8 is similar to FIG. 7 except that electrode D in FIG. 7 has beenintentionally divided into two separate electrodes D1 and D2. D1 and D2do not overlap and are separated by a distance L9. Electrodes C and D1are separated by distance L1*. Electrodes D2 and E are separated by thedistance L2*. If D(1) and D(2) overlap, then the invention has the usualconfiguration described in FIGS. 1, 3, 4, 5, 6, and 7. Then consider thesituation wherein electrodes D(1) and D(2) do not overlap. Suppose theyare separated by 1 inch. Then suppose that the separation distancebetween C to D(1) is 20 inches and suppose that the separation distancebetween D(2) to E is also 20 inches. Then clearly, the invention willstill work, although there will be some error in the current leakagemeasurement caused by the lack of measurement information from the 1inch segment. Perhaps the error shall be on the order of 1 inch dividedby 20 inches, or on the order of an approximate 5% error. FIG. 8 showsan apparatus having four spaced apart voltage measurement electrodesthat compensates for casing thickness variations and for errors inplacements of electrodes by providing measurements of the casingresistance R1 between electrodes C and D1 at the frequency of F(2) byPSD 2 and by providing measurements of the casing resistance R2 betweenelectrodes D2 and E at the frequency F(2) by PSD 3.

FIG. 8 may be operated in a particularly simple manner. The signalbetween electrodes C-D1 can be used to control current flowing along thecasing at the frequency F(1) (by using electronics, not shown, of thetype used to control currents in FIG. 6). Then the signal betweenelectrodes D2-E can be used to measure information related to currentflow along the casing and into the formation at the frequency of F(1).Despite the fact that electrodes C-D1 are used to "control current",nonetheless, the apparatus so described requires at least 3 spaced apartvoltage measurement electrodes and is therefore another embodiment ofthe invention herein.

FIG. 9 shows certain changes to the apparatus defined in FIG. 8. Changesfrom FIG. 8 includes cables 88 and 90 that are meant to convey signalsto the appropriate phase sensitive detectors shown in FIG. 8 for thepurposes of simplicity; extra variable resistor labeled with legend"VR1" placed in series with current meter labeled with legend "I1"connected to cable 92 that provides current at the frequency of F(1) tothe upper current conducting electrode here defined as A1; extravariable resistor labeled with legend "VR2" placed in series withanother current meter labeled with legend "I3" connected to cable 94that provides current at the frequency of F(1) to new electrode A2.Electrodes H and F are shown connected to cables 98 and 100 respectivelywhich operate as shown in FIG. 8, but many of the details are omitted inFIG. 9 in the interest of simplicity. In FIG. 9, current at thefrequency of F(2) is passed between electrodes H and F as in FIG. 8which provides first compensation information related to current flowthrough the casing resistance ("R1") between electrodes C-D1 and secondcompensation information related to current flow through the casingresistance ("R2") between electrodes D2-E, although many of the detailsare not shown in FIG. 9 for the purposes of simplicity. The purpose ofelectrodes A1 and A2 in FIG. 9 are to provide simultaneously upward anddownward flowing currents along the casing at the frequency of F(1).Such simultaneously upward and downward flowing currents along thecasing are hereinafter defined as "counter-flowing currents". Suchcounter-flowing currents in the vicinity of the voltage measurementelectrodes C, D1, D2, and E minimize the "common mode signal" input tothe amplifiers A1 and A2. Therefore, the signal output of amplifiers A1and A2 in the presence of such counter-flowing currents tends to be moreresponsive to the current actually flowing into formation and lessresponsive to the relatively larger currents flowing along the casing.Other apparatus showing methods of introducing counter-flowing currentson the casing include FIGS. 22 and 23 of Ser. No. 07/089,697 , now U.S.Pat. No. 4,882,542, {Vail(542)}. The current actually flowing into theformation at the frequency of F(1) generates voltages across amplifiersA1 and A2 responsive to the current flow into formation that results inmeasurement information at the frequency of F(1) from phase sensitivedetectors as shown in FIG. 8. That measurement information is used todetermine a magnitude relating to formation resistivity, includinginformation related to the resistivity of the adjacent geologicalformation.

FIG. 10 improves the measurement accuracy of the apparatus defined inFIG. 9. FIG. 10 is similar to FIG. 9 except that in FIG. 10 extravoltage measurements P, Q, R, and S have been added. The purpose ofadditional voltage measurement electrodes P and Q are to sense thecurrent flowing along the casing at the frequency of F(1) between P andQ. Further electronics, not shown, are used to control the variableresistor VR1 such that the current flowing along the casing remainsrelatively constant at the frequency of F(1). Please recall thatelectrodes H and F are used to conduct current along the casing at thefrequency of F(2) and therefore, measurements of the potentialdifference between P and Q can be used to measure the casing resistancebetween P and Q that is called "R3" which is therefore used as necessaryinformation to keep the current flowing at the frequency F(1) throughR3. FIG. 6 has already provided means to maintain equality of currentsflowing along the casing, and similar apparatus can be adapted herein tomaintain the equality of current flow at the frequency of F(1) between Pand Q. Similarly comments can be made regarding new electrodes R and Swhich can be used to keep the current flowing along the casing at thefrequency of F(1) constant through the casing resistance betweenelectrodes R and S, that is "R4" by controlling the variable resistorVR2. If the current flowing through R3 at F(1) is held constant as thedevice vertically logs the well, then that shall serve to minimize theinfluence of the lack of information caused by the separation ofelectrodes D1 and D2. Similarly, if the current flowing through R4 atF(1) is held constant, that too serves to minimize the influence of thelack of information caused by the separation between electrodes D1 andD2. Consequently, extra current control means have been provided tocontrol the current flow along the casing at the F(1) to minimize theinfluence of the lack of information from portions of the casing havingno voltage measurement electrodes present. With suitably addedamplifiers, these new electrode pairs can be used to independentlymonitor the counter-flowing currents at the measurement frequency at thepositions shown. In particular, electrode pairs P-Q and R-S can beprovided with amplifiers and feedback circuitry that drives the currentsto A1 and A2 such that the counter-flowing current at the measurementfrequency (for example, 1 Hz) is driven near zero across the voltagemeasurement electrodes C-D1 and D2-E. Regardless of the details ofoperation chosen however, the invention disclosed in FIG. 10 providesfour spaced electrodes means that provides measurement informationrelated to current flow into formation, and respectively, first andsecond compensation information related to measurements of R1 and R2between respectively electrodes C-D, and D-E that are used to determinea magnitude related to formation resistivity. Altogether, FIG. 10 showsa total of 8 each voltage measurement electrodes operated as pairs ofvoltage measurement electrodes.

FIG. 11 is similar to FIG. 10 except that electrodes D1 and D2 have beenre-combined back into one single electrode D herein. However, the extrapotential voltage measurement electrodes P-Q, and R-S remain in FIG. 11to maintain equality of the magnitude of the counter-flowing currentsalong the casing at the frequency of F(1). Maintaining the equality ofcounter-flowing currents along the casing at F(1), and ideally causingthe counter-flowing currents to approach the limit of zero net currentflowing up or down the casing at the frequency of F(1) will result inimproved measurement accuracy. Regardless of the details of operationchosen however, the invention disclosed in FIG. 11 provides a minimum of3 spaced electrodes means that provides measurement information relatedto current flow into formation, and respectively, first and secondcompensation information related to measurements of R1 and R2 betweenrespectively electrodes C-D, and D-E that are used to determine amagnitude related to formation resistivity. Altogether, FIG. 11 shows atotal of 7 each voltage measurement electrodes operated as 4 pairs ofvoltage measurement electrodes.

FIG. 12 is similar to FIG. 11 except that the extra potential voltagemeasurement electrodes P-Q and R-S have been removed. It should be notedthat the apparatus defined in FIG. 12 results in knowledge of themeasurement current leaking into formation, knowledge of the resistanceR1 between voltage measurement electrodes C-D, and the knowledge of theresistance R2 between voltage measurement electrodes D-E. Therefore, theapparatus in FIG. 12 provides knowledge of the net current at F(1)flowing through resistor R1 between electrodes C-D. Similarly, theapparatus in FIG. 12 provides knowledge of the net current at F(1)flowing through resistor R2 between electrodes D-E. Extra controlcircuitry, not shown, can be adapted as in FIG. 6 to minimize the netcounter-flowing currents flowing by the combined resistors R1 and R2 toimprove measurement accuracy. Regardless of the details of operationchosen however, the invention disclosed in FIG. 12 provides a minimum of3 spaced apart electrode means that provide measurement informationrelated to current flow into formation, and respectively, first andsecond compensation information related to measurements of R1 and R2between respectively electrodes C-D, and D-E that are used to determinea magnitude related to formation resistivity.

The apparatus in FIG. 12 may be operated in a particularly simplemanner. Information from pair C-D can be used to control the magnitudeof the current flowing along the casing at the frequency of F(1), andkeep it constant. Then information from pair D-E can be used to infergeophysical parameters from measurements of the current at the frequencyof F(1). Despite the fact that the first pair C-D is used primarilyherein "to control current", the apparatus so described nonethelessrequires 3 spaced apart voltage measurement electrodes which engage theinterior of the casing and is therefore simply another embodiment of theinvention herein.

FIG. 13 is functionally identical to FIG. 26 from Ser. No. 07/089,697that is U.S. Pat. No. 4,882,542, showing an apparatus having multiplevoltage measurement electrodes engaging the interior of the casing thatis marked with the legend "Prior Art". Individual potential voltagemeasurement electrodes k, l, m, n, o, p, q, r, s, and t electricallyengage the casing. In principle, any total number Z of such potentialvoltage measuring electrodes can be made to electrically engage theinterior of the casing. During the calibration step described inVail(542), current is passed along the casing resulting in the knowledgeof the respective casing resistances between each potential voltagemeasurement electrode. The casing resistance between electrodes k and lis defined herein as R(k,l). The casing resistance between electrodes land m is defined herein as R(l,m). The casing resistance between m and nis defined herein R(m,n). The casing resistance between n and o isdefined herein as R(n,o). By analogy, the casing resistances R(o,p),R(p,q), R(q,r), R(r,s) and R(s,t) are defined herein. In principle, anynumber of casing resistances can be defined for any number Z ofelectrodes which electrically engage the interior of the casing. Thedistance along the casing between electrodes k and l is defined hereinas L(k,l). The distance along the casing between electrodes l and m isdefined herein as L(l,m). The distance along the casing betweenelectrodes m and n is defined herein as L(m,n). The distance along thecasing between electrodes n and o is defined herein as L(n,o). Byanalogy, the distances of separation of appropriate electrodes aredefined herein as L(o,p), L(p,q), L(q,r), L(r,s,) and L(s,t). Inprinciple, any number of distances can be defined between any number Zelectrodes which electrically engage the interior of the casing. Thedistance of separation between electrodes can be chosen to be anydistance. They may be chosen to be equal or they can be chosen not to beequal, depending upon chosen function. For example, L(k,l) can be chosento be 3 inches. L(l,m) can be chosen to be 6 inches. L(m,n) can bechosen to be 12 inches. L(n,o) can be chosen to be 20 inches. L(o,p) canbe chosen to be 52 inches. L(p,q) can be chosen to be 60 inches. L(q,r)can be chosen to be 120 inches. Further, electrodes s and t can bedisconnected. Such an array can measure the potential voltagedistribution along the casing or the potential voltage profile along thecasing in response to calibration currents primarily flowing along thecasing and in response to the measurement currents flowing along thecasing and into the formation. The calibration current can be at chosento be the same frequency as the measurement current as originallydescribed in Vail(989) or can be at a different frequency as describedin Vail(626). The above described variable spacing can be used to inferthe vertical and radial variations of the geological formation, thevertical distribution of geological beds, and other geologicalinformation. Regardless of the details of operation chosen however, theinvention disclosed in FIG. 13 provides a minimum of 3 spaced apartvoltage measurement electrode means that provide measurement informationrelated to current flow into formation, and respectively, first andsecond compensation information related to measurements of at least twocasing resistances respectively between the three voltage measurementelectrodes, wherein said measurement information and the first andsecond compensation information are used to determine a magnituderelated to formation resistivity. FIG. 12 and the text herein furthershows that a plurality of spaced apart electrodes along the casing,which may be chosen to be spaced at various different intervals, providemultiple measurements of quantities related to current flow intoformation, and provide multiple measurements of the resistances of thecasing spanned by the particular number of chosen spaced apartelectrodes that may be used to infer geophysical information includingthe resistivity of the adjacent formation.

It should also be noted that Ser. No. 07/089,697, now U.S. Pat. No.4,882,542, describes many different means to measure voltage profiles onthe casing including those shown in FIG. 25, 26, 27, 28, and 29 therein.Those drawings describe several other apparatus geometries havingmultiple electrodes.

Various embodiments of the invention herein provide many differentmanners to introduce current onto the casing, a portion of which issubsequently conducted through formation. Various embodiments hereinprovide many different methods to measure voltage levels at a pluralityof many points on the casing to provide a potential voltage profilealong the casing which may be interpreted to measure the current leakingoff the exterior of the casing from within a finite vertical section ofthe casing. Regardless of the details of operation chosen however, theinvention herein disclosed provides a minimum of 3 spaced apart voltagemeasurement electrode means that provides measurement informationrelated to current flow into the geological formation, and respectively,first and second compensation information related to measurements of atleast two separate casing resistances between the three spaced apartvoltage measurement electrodes, wherein the measurement information andthe first and second compensation information are used to determine amagnitude related to formation resistivity.

While the above description contains many specificities, these shouldnot be construed as limitations on the scope of the invention, butrather as exemplification of preferred embodiments thereto. As has beenbriefly described, there are many possible variations. Accordingly, thescope of the invention should be determined not only by the embodimentsillustrated, but by the appended claims and their legal equivalents.

What is claimed is:
 1. An apparatus for determining the resistivity of ageological formation from within a cased well, comprising:a firstelectrode that electrically engages a particular section of casing at aspecific depth within the well for receiving first signals havingvoltage related information; a second electrode that electricallyengages the particular section of casing for receiving second signalshaving voltage related information located a first distance above saidfirst electrode wherein the magnitude of the resistance of the portionof casing between said first and second electrodes is the firstresistance; a third electrode that electrically engages the particularsection of casing for receiving third signals having voltage relatedinformation located a second distance below said first electrode whereinthe magnitude of the resistance of the portion of casing between saidfirst and third electrodes is the second resistance; current generatingmeans for causing at least a selected one of a first current to flowinto the geological formation and a second current to flow along theparticular section of casing; and means for processing said first,second and third signals from said first, second and third electrodemeans for use in determining the resistivity of the formation ofinterest, said means for processing taking into account a magnituderelating to the values of said first resistance and said secondresistance so that inaccuracy associated with the determination of theresistivity is reduced.
 2. A method for determining the resistivity of ageological formation from within a cased well comprising:providing anapparatus having a first electrode that electrically engages aparticular section of casing for receiving first voltage related signalsat a specific depth within the well; said apparatus having a secondelectrode that electrically engages the particular section of casing forreceiving second voltage related signals located a first distance abovesaid first electrode wherein the magnitude of the resistance of theportion of casing between said first and second electrodes is the firstresistance; and said apparatus having a third electrode thatelectrically engages the particular section of casing for receivingthird voltage related signals located a second distance below said firstelectrode wherein the magnitude of the resistance of the portion ofcasing between said first and third electrodes is the second resistance;causing a first current to flow into the geological formation from theparticular section of casing; causing a second current to flow along theparticular section of casing; obtaining said first, second, and thirdvoltage related signals while conducting said first current intoformation during the measurement step; determining the magnitude of saidfirst resistance using at least a selected one of said first current andsaid second current; determining the magnitude of said second resistanceusing at least a selected one of said first current and said secondcurrent; and processing the voltage related signals from each of saidfirst, second and third electrodes obtained during the measurement stepfor use in determining the resistivity of the geological formation ofinterest, said processing taking into account the determined magnitudesof said first resistance and said second resistance to reduce theinaccuracy associated with the determination of the resistivity of thegeological formation of interest.